Doubly differential single and multiple ionization of krypton by electron impact

Abstract

Differential measurements for single and multiple ionization of Kr by 240 and $500\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ electron impact are presented. Using a pulsed extraction field, ${\mathrm{Kr}}^{+}$, ${\mathrm{Kr}}^{2+}$, and ${\mathrm{Kr}}^{3+}$ ions were measured in coincidence with scattered electrons for energy losses up to $120\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and scattering angles between 16\ifmmode^\circ\else\textdegree\fi{} and 90\ifmmode^\circ\else\textdegree\fi{}. Scaling properties of the doubly differential cross sections (DDCS) are investigated as a function of energy loss, scattering angle, and momentum transfer. It is shown that scaling the DDCS as outlined by Kim and Inokuti and plotting them versus a parameter consisting of the momentum transfer divided by the square root of the impact energy times $1\ensuremath{-}\mathrm{cos}(\ensuremath{\theta})$, where $\ensuremath{\theta}$ is the scattering angle, yielded similar curves, but with different magnitudes, for single and multiple ionization. Normalizing these curves together produced two universal curves, one appropriate for single and multiple electron emission at larger scattering angles $(\ensuremath{\theta}\ensuremath{\geqslant}30\ifmmode^\circ\else\textdegree\fi{})$ and one appropriate for small scattering angles $(\ensuremath{\theta}<30\ifmmode^\circ\else\textdegree\fi{})$.